Question

HELP ME SOLVE THIS PROBLEM!

BEST ANSWER WILL BE MARKED AS BRAINLIEST!

Answer 1

Note: Here, I am writing θ as A.

Now,

$Given : \frac{cosecA + cotA}{cosecA - cotA}$

On rationalizing, we get

$=> \frac{cosecA + cotA}{cosecA - cotA}*\frac{cosecA + cotA}{cosecA + cotA}$

$=>\frac{(cosecA + cotA)^2}{cosec^2A - cot^2A}$

We know that cosec^2A - cot^2A = 1

$=>(cosecA + cotA)^2$

$=>cosec^2A + cot^2A + 2cosec^2AcotA$

We know that cosec^2A - cot^2A = 1 (or) cosec^2A = 1 + cot^2A

⇒ (1 + cot^2A) + cot^2A + 2cosecAcotA

⇒ 1 + 2cot^2A + 2cosec^2AcotA

Hope it helps!